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In 2000 Kuzmin competed in the World Rowing Junior Championships in the single sculls event earning 12 position. In 2002 he competed in the U-23 World Regatta with Andrei Jämsä in the double sculls event earning 7th position.

His first appearance in the Olympic Games was in Athens 2004, where he competed in the quadruple sculls event with Andrei Jämsä, Andrei Šilin and Oleg Vinogradov earning 9th position overall.

Kuzmin's second appearance at the Olympics was in Beijing 2008 where he competed in the quadruple sculls event with Allar Raja, Vladimir Latin and Kaspar Taimsoo. The men were 4th in their preliminary heat and won the repechage. In the semifinals they finished fourth and did not get to Final A. The final place was 9th as they finished third in Final B.